A particle of mass m is released from rest at a height y = h. (a) Write the Hamiltonian of the system. (b) Write the Hamilton-Jacobi equation for Hamilton’s principal equation S. (c) Assume that S = W(y, α) − αt. Using the Hamilton-Jacobi method, find y(t) as a function of the initial conditions.
A particle of mass m is released from rest at a height y = h. (a) Write the Hamiltonian of the system. (b) Write the Hamilton-Jacobi equation for Hamilton’s principal equation S. (c) Assume that S = W(y, α) − αt. Using the Hamilton-Jacobi method, find y(t) as a function of the initial conditions.
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A particle of mass m is released from rest at a height y = h.
(a) Write the Hamiltonian of the system.
(b) Write the Hamilton-Jacobi equation for Hamilton’s principal equation S.
(c) Assume that S = W(y, α) − αt. Using the Hamilton-Jacobi method, find y(t) as a function of the initial
conditions.
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